Educational Process Mining¶

https://archive-beta.ics.uci.edu/dataset/346/educational+process+mining+epm+a+learning+analytics+data+set

Educational Process Mining (EPM): A Learning Analytics Data Set. (2015). UCI Machine Learning Repository.

This notebook includes feature evaluation with statsmodels and dmatrices and with Pipelines.

In [1]:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

import seaborn as sns
In [2]:
from patsy import dmatrices

from numpy import arange

from sklearn.preprocessing import OneHotEncoder

from sklearn.compose import ColumnTransformer

from sklearn.model_selection import cross_val_score

from sklearn.model_selection import KFold

from sklearn.preprocessing import StandardScaler

from sklearn.decomposition import PCA

from sklearn.preprocessing import PolynomialFeatures

from sklearn.linear_model import ElasticNet

from sklearn.model_selection import GridSearchCV

from sklearn.pipeline import Pipeline

Load the data from github repository¶

In [3]:
inputs_path = 'https://raw.githubusercontent.com/lisaover/CMPINF2120_project/main/tp_sqrt_inputs_df.csv'
interim_path = 'https://raw.githubusercontent.com/lisaover/CMPINF2120_project/main/interim_df.csv'
final_path = 'https://raw.githubusercontent.com/lisaover/CMPINF2120_project/main/final_df.csv'
pts_path = 'https://raw.githubusercontent.com/lisaover/CMPINF2120_project/main/final_points_lookup.csv'
In [4]:
inputs_init = pd.read_csv(inputs_path)
In [5]:
interim_init = pd.read_csv(interim_path)
In [6]:
final_init = pd.read_csv(final_path)
In [7]:
pts_final_lookup = pd.read_csv(pts_path)
In [8]:
inputs_init.columns
Out[8]:
Index(['sess', 'sid', 'actv_grp', 'total_ms_tp000_sqrt', 'mw_tp000_sqrt',
       'mwc_tp000_sqrt', 'mcl_tp000_sqrt', 'mcr_tp000_sqrt', 'mm_tp000_sqrt',
       'ks_tp000_sqrt', 'total_ms_tp010_sqrt', 'mw_tp010_sqrt',
       'mwc_tp010_sqrt', 'mcl_tp010_sqrt', 'mcr_tp010_sqrt', 'mm_tp010_sqrt',
       'ks_tp010_sqrt', 'total_ms_tp020_sqrt', 'mw_tp020_sqrt',
       'mwc_tp020_sqrt', 'mcl_tp020_sqrt', 'mcr_tp020_sqrt', 'mm_tp020_sqrt',
       'ks_tp020_sqrt', 'total_ms_tp030_sqrt', 'mw_tp030_sqrt',
       'mwc_tp030_sqrt', 'mcl_tp030_sqrt', 'mcr_tp030_sqrt', 'mm_tp030_sqrt',
       'ks_tp030_sqrt', 'total_ms_tp040_sqrt', 'mw_tp040_sqrt',
       'mwc_tp040_sqrt', 'mcl_tp040_sqrt', 'mcr_tp040_sqrt', 'mm_tp040_sqrt',
       'ks_tp040_sqrt', 'total_ms_tp050_sqrt', 'mw_tp050_sqrt',
       'mwc_tp050_sqrt', 'mcl_tp050_sqrt', 'mcr_tp050_sqrt', 'mm_tp050_sqrt',
       'ks_tp050_sqrt', 'total_ms_tp060_sqrt', 'mw_tp060_sqrt',
       'mwc_tp060_sqrt', 'mcl_tp060_sqrt', 'mcr_tp060_sqrt', 'mm_tp060_sqrt',
       'ks_tp060_sqrt', 'total_ms_tp070_sqrt', 'mw_tp070_sqrt',
       'mwc_tp070_sqrt', 'mcl_tp070_sqrt', 'mcr_tp070_sqrt', 'mm_tp070_sqrt',
       'ks_tp070_sqrt', 'total_ms_tp080_sqrt', 'mw_tp080_sqrt',
       'mwc_tp080_sqrt', 'mcl_tp080_sqrt', 'mcr_tp080_sqrt', 'mm_tp080_sqrt',
       'ks_tp080_sqrt', 'total_ms_tp090_sqrt', 'mw_tp090_sqrt',
       'mwc_tp090_sqrt', 'mcl_tp090_sqrt', 'mcr_tp090_sqrt', 'mm_tp090_sqrt',
       'ks_tp090_sqrt', 'total_ms_tp100_sqrt', 'mw_tp100_sqrt',
       'mwc_tp100_sqrt', 'mcl_tp100_sqrt', 'mcr_tp100_sqrt', 'mm_tp100_sqrt',
       'ks_tp100_sqrt'],
      dtype='object')
In [9]:
interim_init.columns
Out[9]:
Index(['sid', 'interim_scr2', 'interim_scr3', 'interim_scr4', 'interim_scr5',
       'interim_scr6'],
      dtype='object')
In [10]:
final_init.columns
Out[10]:
Index(['sid', 'Es_1q1', 'Es_1q2', 'Es_2q1', 'Es_2q2', 'Es_3q1', 'Es_3q2',
       'Es_3q3', 'Es_3q4', 'Es_3q5', 'Es_4q1', 'Es_4q2', 'Es_5q1', 'Es_5q2',
       'Es_5q3', 'Es_6q1', 'Es_6q2', 'final_score'],
      dtype='object')
In [11]:
pts_final_lookup.columns
Out[11]:
Index(['question', 'question_points'], dtype='object')
In [12]:
inputs_init.isna().sum()
Out[12]:
sess                   0
sid                    0
actv_grp               0
total_ms_tp000_sqrt    0
mw_tp000_sqrt          0
                      ..
mwc_tp100_sqrt         0
mcl_tp100_sqrt         0
mcr_tp100_sqrt         0
mm_tp100_sqrt          0
ks_tp100_sqrt          0
Length: 80, dtype: int64
In [13]:
inputs_init.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 4248 entries, 0 to 4247
Data columns (total 80 columns):
 #   Column               Non-Null Count  Dtype  
---  ------               --------------  -----  
 0   sess                 4248 non-null   int64  
 1   sid                  4248 non-null   int64  
 2   actv_grp             4248 non-null   object 
 3   total_ms_tp000_sqrt  4248 non-null   float64
 4   mw_tp000_sqrt        4248 non-null   float64
 5   mwc_tp000_sqrt       4248 non-null   float64
 6   mcl_tp000_sqrt       4248 non-null   float64
 7   mcr_tp000_sqrt       4248 non-null   float64
 8   mm_tp000_sqrt        4248 non-null   float64
 9   ks_tp000_sqrt        4248 non-null   float64
 10  total_ms_tp010_sqrt  4248 non-null   float64
 11  mw_tp010_sqrt        4248 non-null   float64
 12  mwc_tp010_sqrt       4248 non-null   float64
 13  mcl_tp010_sqrt       4248 non-null   float64
 14  mcr_tp010_sqrt       4248 non-null   float64
 15  mm_tp010_sqrt        4248 non-null   float64
 16  ks_tp010_sqrt        4248 non-null   float64
 17  total_ms_tp020_sqrt  4248 non-null   float64
 18  mw_tp020_sqrt        4248 non-null   float64
 19  mwc_tp020_sqrt       4248 non-null   float64
 20  mcl_tp020_sqrt       4248 non-null   float64
 21  mcr_tp020_sqrt       4248 non-null   float64
 22  mm_tp020_sqrt        4248 non-null   float64
 23  ks_tp020_sqrt        4248 non-null   float64
 24  total_ms_tp030_sqrt  4248 non-null   float64
 25  mw_tp030_sqrt        4248 non-null   float64
 26  mwc_tp030_sqrt       4248 non-null   float64
 27  mcl_tp030_sqrt       4248 non-null   float64
 28  mcr_tp030_sqrt       4248 non-null   float64
 29  mm_tp030_sqrt        4248 non-null   float64
 30  ks_tp030_sqrt        4248 non-null   float64
 31  total_ms_tp040_sqrt  4248 non-null   float64
 32  mw_tp040_sqrt        4248 non-null   float64
 33  mwc_tp040_sqrt       4248 non-null   float64
 34  mcl_tp040_sqrt       4248 non-null   float64
 35  mcr_tp040_sqrt       4248 non-null   float64
 36  mm_tp040_sqrt        4248 non-null   float64
 37  ks_tp040_sqrt        4248 non-null   float64
 38  total_ms_tp050_sqrt  4248 non-null   float64
 39  mw_tp050_sqrt        4248 non-null   float64
 40  mwc_tp050_sqrt       4248 non-null   float64
 41  mcl_tp050_sqrt       4248 non-null   float64
 42  mcr_tp050_sqrt       4248 non-null   float64
 43  mm_tp050_sqrt        4248 non-null   float64
 44  ks_tp050_sqrt        4248 non-null   float64
 45  total_ms_tp060_sqrt  4248 non-null   float64
 46  mw_tp060_sqrt        4248 non-null   float64
 47  mwc_tp060_sqrt       4248 non-null   float64
 48  mcl_tp060_sqrt       4248 non-null   float64
 49  mcr_tp060_sqrt       4248 non-null   float64
 50  mm_tp060_sqrt        4248 non-null   float64
 51  ks_tp060_sqrt        4248 non-null   float64
 52  total_ms_tp070_sqrt  4248 non-null   float64
 53  mw_tp070_sqrt        4248 non-null   float64
 54  mwc_tp070_sqrt       4248 non-null   float64
 55  mcl_tp070_sqrt       4248 non-null   float64
 56  mcr_tp070_sqrt       4248 non-null   float64
 57  mm_tp070_sqrt        4248 non-null   float64
 58  ks_tp070_sqrt        4248 non-null   float64
 59  total_ms_tp080_sqrt  4248 non-null   float64
 60  mw_tp080_sqrt        4248 non-null   float64
 61  mwc_tp080_sqrt       4248 non-null   float64
 62  mcl_tp080_sqrt       4248 non-null   float64
 63  mcr_tp080_sqrt       4248 non-null   float64
 64  mm_tp080_sqrt        4248 non-null   float64
 65  ks_tp080_sqrt        4248 non-null   float64
 66  total_ms_tp090_sqrt  4248 non-null   float64
 67  mw_tp090_sqrt        4248 non-null   float64
 68  mwc_tp090_sqrt       4248 non-null   float64
 69  mcl_tp090_sqrt       4248 non-null   float64
 70  mcr_tp090_sqrt       4248 non-null   float64
 71  mm_tp090_sqrt        4248 non-null   float64
 72  ks_tp090_sqrt        4248 non-null   float64
 73  total_ms_tp100_sqrt  4248 non-null   float64
 74  mw_tp100_sqrt        4248 non-null   float64
 75  mwc_tp100_sqrt       4248 non-null   float64
 76  mcl_tp100_sqrt       4248 non-null   float64
 77  mcr_tp100_sqrt       4248 non-null   float64
 78  mm_tp100_sqrt        4248 non-null   float64
 79  ks_tp100_sqrt        4248 non-null   float64
dtypes: float64(77), int64(2), object(1)
memory usage: 2.6+ MB
In [14]:
inputs_init['sid'] = inputs_init['sid'].astype('object')
inputs_init['sess'] = inputs_init['sess'].astype('object')
In [15]:
inputs_df = inputs_init.copy()
In [16]:
interim_df = interim_init.copy()

Melt interim_df and create a session variable to merge with inputs_df by session and student_id¶

In [17]:
interim_lf = interim_df.melt( id_vars=['sid']).\
             rename(columns={"variable": "interim_sess", "value": "interim_scr"}).\
             copy()
In [18]:
interim_lf['sess'] = interim_lf.interim_sess.str.extract('(\d+)')
In [19]:
interim_lf
Out[19]:
sid interim_sess interim_scr sess
0 1 interim_scr2 5.0 2
1 2 interim_scr2 4.0 2
2 3 interim_scr2 3.5 2
3 4 interim_scr2 6.0 2
4 5 interim_scr2 5.0 2
... ... ... ... ...
570 111 interim_scr6 0.0 6
571 112 interim_scr6 0.0 6
572 113 interim_scr6 0.0 6
573 114 interim_scr6 0.0 6
574 115 interim_scr6 0.0 6

575 rows × 4 columns

In [20]:
interim_lf.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 575 entries, 0 to 574
Data columns (total 4 columns):
 #   Column        Non-Null Count  Dtype  
---  ------        --------------  -----  
 0   sid           575 non-null    int64  
 1   interim_sess  575 non-null    object 
 2   interim_scr   575 non-null    float64
 3   sess          575 non-null    object 
dtypes: float64(1), int64(1), object(2)
memory usage: 18.1+ KB

Merge inputs_df with interim_lf¶

In [21]:
interim_lf.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 575 entries, 0 to 574
Data columns (total 4 columns):
 #   Column        Non-Null Count  Dtype  
---  ------        --------------  -----  
 0   sid           575 non-null    int64  
 1   interim_sess  575 non-null    object 
 2   interim_scr   575 non-null    float64
 3   sess          575 non-null    object 
dtypes: float64(1), int64(1), object(2)
memory usage: 18.1+ KB
In [22]:
interim_lf.isna().sum()
Out[22]:
sid             0
interim_sess    0
interim_scr     0
sess            0
dtype: int64
In [23]:
interim_lf
Out[23]:
sid interim_sess interim_scr sess
0 1 interim_scr2 5.0 2
1 2 interim_scr2 4.0 2
2 3 interim_scr2 3.5 2
3 4 interim_scr2 6.0 2
4 5 interim_scr2 5.0 2
... ... ... ... ...
570 111 interim_scr6 0.0 6
571 112 interim_scr6 0.0 6
572 113 interim_scr6 0.0 6
573 114 interim_scr6 0.0 6
574 115 interim_scr6 0.0 6

575 rows × 4 columns

In [24]:
interim_lf['sess'] = interim_lf['sess'].astype('int')
In [25]:
io_init = pd.merge(inputs_df, interim_lf, on=['sid', 'sess'], how='left').drop(columns=['interim_sess'])
In [26]:
io_df = io_init.loc[io_init.sess != 1].dropna().copy()
In [27]:
io_df.info()

<class 'pandas.core.frame.DataFrame'>
Int64Index: 3642 entries, 606 to 4247
Data columns (total 81 columns):
 #   Column               Non-Null Count  Dtype  
---  ------               --------------  -----  
 0   sess                 3642 non-null   object 
 1   sid                  3642 non-null   object 
 2   actv_grp             3642 non-null   object 
 3   total_ms_tp000_sqrt  3642 non-null   float64
 4   mw_tp000_sqrt        3642 non-null   float64
 5   mwc_tp000_sqrt       3642 non-null   float64
 6   mcl_tp000_sqrt       3642 non-null   float64
 7   mcr_tp000_sqrt       3642 non-null   float64
 8   mm_tp000_sqrt        3642 non-null   float64
 9   ks_tp000_sqrt        3642 non-null   float64
 10  total_ms_tp010_sqrt  3642 non-null   float64
 11  mw_tp010_sqrt        3642 non-null   float64
 12  mwc_tp010_sqrt       3642 non-null   float64
 13  mcl_tp010_sqrt       3642 non-null   float64
 14  mcr_tp010_sqrt       3642 non-null   float64
 15  mm_tp010_sqrt        3642 non-null   float64
 16  ks_tp010_sqrt        3642 non-null   float64
 17  total_ms_tp020_sqrt  3642 non-null   float64
 18  mw_tp020_sqrt        3642 non-null   float64
 19  mwc_tp020_sqrt       3642 non-null   float64
 20  mcl_tp020_sqrt       3642 non-null   float64
 21  mcr_tp020_sqrt       3642 non-null   float64
 22  mm_tp020_sqrt        3642 non-null   float64
 23  ks_tp020_sqrt        3642 non-null   float64
 24  total_ms_tp030_sqrt  3642 non-null   float64
 25  mw_tp030_sqrt        3642 non-null   float64
 26  mwc_tp030_sqrt       3642 non-null   float64
 27  mcl_tp030_sqrt       3642 non-null   float64
 28  mcr_tp030_sqrt       3642 non-null   float64
 29  mm_tp030_sqrt        3642 non-null   float64
 30  ks_tp030_sqrt        3642 non-null   float64
 31  total_ms_tp040_sqrt  3642 non-null   float64
 32  mw_tp040_sqrt        3642 non-null   float64
 33  mwc_tp040_sqrt       3642 non-null   float64
 34  mcl_tp040_sqrt       3642 non-null   float64
 35  mcr_tp040_sqrt       3642 non-null   float64
 36  mm_tp040_sqrt        3642 non-null   float64
 37  ks_tp040_sqrt        3642 non-null   float64
 38  total_ms_tp050_sqrt  3642 non-null   float64
 39  mw_tp050_sqrt        3642 non-null   float64
 40  mwc_tp050_sqrt       3642 non-null   float64
 41  mcl_tp050_sqrt       3642 non-null   float64
 42  mcr_tp050_sqrt       3642 non-null   float64
 43  mm_tp050_sqrt        3642 non-null   float64
 44  ks_tp050_sqrt        3642 non-null   float64
 45  total_ms_tp060_sqrt  3642 non-null   float64
 46  mw_tp060_sqrt        3642 non-null   float64
 47  mwc_tp060_sqrt       3642 non-null   float64
 48  mcl_tp060_sqrt       3642 non-null   float64
 49  mcr_tp060_sqrt       3642 non-null   float64
 50  mm_tp060_sqrt        3642 non-null   float64
 51  ks_tp060_sqrt        3642 non-null   float64
 52  total_ms_tp070_sqrt  3642 non-null   float64
 53  mw_tp070_sqrt        3642 non-null   float64
 54  mwc_tp070_sqrt       3642 non-null   float64
 55  mcl_tp070_sqrt       3642 non-null   float64
 56  mcr_tp070_sqrt       3642 non-null   float64
 57  mm_tp070_sqrt        3642 non-null   float64
 58  ks_tp070_sqrt        3642 non-null   float64
 59  total_ms_tp080_sqrt  3642 non-null   float64
 60  mw_tp080_sqrt        3642 non-null   float64
 61  mwc_tp080_sqrt       3642 non-null   float64
 62  mcl_tp080_sqrt       3642 non-null   float64
 63  mcr_tp080_sqrt       3642 non-null   float64
 64  mm_tp080_sqrt        3642 non-null   float64
 65  ks_tp080_sqrt        3642 non-null   float64
 66  total_ms_tp090_sqrt  3642 non-null   float64
 67  mw_tp090_sqrt        3642 non-null   float64
 68  mwc_tp090_sqrt       3642 non-null   float64
 69  mcl_tp090_sqrt       3642 non-null   float64
 70  mcr_tp090_sqrt       3642 non-null   float64
 71  mm_tp090_sqrt        3642 non-null   float64
 72  ks_tp090_sqrt        3642 non-null   float64
 73  total_ms_tp100_sqrt  3642 non-null   float64
 74  mw_tp100_sqrt        3642 non-null   float64
 75  mwc_tp100_sqrt       3642 non-null   float64
 76  mcl_tp100_sqrt       3642 non-null   float64
 77  mcr_tp100_sqrt       3642 non-null   float64
 78  mm_tp100_sqrt        3642 non-null   float64
 79  ks_tp100_sqrt        3642 non-null   float64
 80  interim_scr          3642 non-null   float64
dtypes: float64(78), object(3)
memory usage: 2.3+ MB
In [28]:
io_df.sess.unique()
Out[28]:
array([2, 3, 4, 5, 6], dtype=object)

Generate the output and input feature arrays using the formula interface¶

In [29]:
io_df.columns
Out[29]:
Index(['sess', 'sid', 'actv_grp', 'total_ms_tp000_sqrt', 'mw_tp000_sqrt',
       'mwc_tp000_sqrt', 'mcl_tp000_sqrt', 'mcr_tp000_sqrt', 'mm_tp000_sqrt',
       'ks_tp000_sqrt', 'total_ms_tp010_sqrt', 'mw_tp010_sqrt',
       'mwc_tp010_sqrt', 'mcl_tp010_sqrt', 'mcr_tp010_sqrt', 'mm_tp010_sqrt',
       'ks_tp010_sqrt', 'total_ms_tp020_sqrt', 'mw_tp020_sqrt',
       'mwc_tp020_sqrt', 'mcl_tp020_sqrt', 'mcr_tp020_sqrt', 'mm_tp020_sqrt',
       'ks_tp020_sqrt', 'total_ms_tp030_sqrt', 'mw_tp030_sqrt',
       'mwc_tp030_sqrt', 'mcl_tp030_sqrt', 'mcr_tp030_sqrt', 'mm_tp030_sqrt',
       'ks_tp030_sqrt', 'total_ms_tp040_sqrt', 'mw_tp040_sqrt',
       'mwc_tp040_sqrt', 'mcl_tp040_sqrt', 'mcr_tp040_sqrt', 'mm_tp040_sqrt',
       'ks_tp040_sqrt', 'total_ms_tp050_sqrt', 'mw_tp050_sqrt',
       'mwc_tp050_sqrt', 'mcl_tp050_sqrt', 'mcr_tp050_sqrt', 'mm_tp050_sqrt',
       'ks_tp050_sqrt', 'total_ms_tp060_sqrt', 'mw_tp060_sqrt',
       'mwc_tp060_sqrt', 'mcl_tp060_sqrt', 'mcr_tp060_sqrt', 'mm_tp060_sqrt',
       'ks_tp060_sqrt', 'total_ms_tp070_sqrt', 'mw_tp070_sqrt',
       'mwc_tp070_sqrt', 'mcl_tp070_sqrt', 'mcr_tp070_sqrt', 'mm_tp070_sqrt',
       'ks_tp070_sqrt', 'total_ms_tp080_sqrt', 'mw_tp080_sqrt',
       'mwc_tp080_sqrt', 'mcl_tp080_sqrt', 'mcr_tp080_sqrt', 'mm_tp080_sqrt',
       'ks_tp080_sqrt', 'total_ms_tp090_sqrt', 'mw_tp090_sqrt',
       'mwc_tp090_sqrt', 'mcl_tp090_sqrt', 'mcr_tp090_sqrt', 'mm_tp090_sqrt',
       'ks_tp090_sqrt', 'total_ms_tp100_sqrt', 'mw_tp100_sqrt',
       'mwc_tp100_sqrt', 'mcl_tp100_sqrt', 'mcr_tp100_sqrt', 'mm_tp100_sqrt',
       'ks_tp100_sqrt', 'interim_scr'],
      dtype='object')
In [30]:
def get_var_list(df, lst):
    temp = []
    for s in lst:
        temp = [j for i in [temp, df.loc[:, df.columns.str.endswith(s)].columns] for j in i] 
    return temp
In [31]:
num_vars = get_var_list(io_df,['sqrt'])
In [32]:
num_vars
Out[32]:
['total_ms_tp000_sqrt',
 'mw_tp000_sqrt',
 'mwc_tp000_sqrt',
 'mcl_tp000_sqrt',
 'mcr_tp000_sqrt',
 'mm_tp000_sqrt',
 'ks_tp000_sqrt',
 'total_ms_tp010_sqrt',
 'mw_tp010_sqrt',
 'mwc_tp010_sqrt',
 'mcl_tp010_sqrt',
 'mcr_tp010_sqrt',
 'mm_tp010_sqrt',
 'ks_tp010_sqrt',
 'total_ms_tp020_sqrt',
 'mw_tp020_sqrt',
 'mwc_tp020_sqrt',
 'mcl_tp020_sqrt',
 'mcr_tp020_sqrt',
 'mm_tp020_sqrt',
 'ks_tp020_sqrt',
 'total_ms_tp030_sqrt',
 'mw_tp030_sqrt',
 'mwc_tp030_sqrt',
 'mcl_tp030_sqrt',
 'mcr_tp030_sqrt',
 'mm_tp030_sqrt',
 'ks_tp030_sqrt',
 'total_ms_tp040_sqrt',
 'mw_tp040_sqrt',
 'mwc_tp040_sqrt',
 'mcl_tp040_sqrt',
 'mcr_tp040_sqrt',
 'mm_tp040_sqrt',
 'ks_tp040_sqrt',
 'total_ms_tp050_sqrt',
 'mw_tp050_sqrt',
 'mwc_tp050_sqrt',
 'mcl_tp050_sqrt',
 'mcr_tp050_sqrt',
 'mm_tp050_sqrt',
 'ks_tp050_sqrt',
 'total_ms_tp060_sqrt',
 'mw_tp060_sqrt',
 'mwc_tp060_sqrt',
 'mcl_tp060_sqrt',
 'mcr_tp060_sqrt',
 'mm_tp060_sqrt',
 'ks_tp060_sqrt',
 'total_ms_tp070_sqrt',
 'mw_tp070_sqrt',
 'mwc_tp070_sqrt',
 'mcl_tp070_sqrt',
 'mcr_tp070_sqrt',
 'mm_tp070_sqrt',
 'ks_tp070_sqrt',
 'total_ms_tp080_sqrt',
 'mw_tp080_sqrt',
 'mwc_tp080_sqrt',
 'mcl_tp080_sqrt',
 'mcr_tp080_sqrt',
 'mm_tp080_sqrt',
 'ks_tp080_sqrt',
 'total_ms_tp090_sqrt',
 'mw_tp090_sqrt',
 'mwc_tp090_sqrt',
 'mcl_tp090_sqrt',
 'mcr_tp090_sqrt',
 'mm_tp090_sqrt',
 'ks_tp090_sqrt',
 'total_ms_tp100_sqrt',
 'mw_tp100_sqrt',
 'mwc_tp100_sqrt',
 'mcl_tp100_sqrt',
 'mcr_tp100_sqrt',
 'mm_tp100_sqrt',
 'ks_tp100_sqrt']
In [33]:
len(num_vars)
Out[33]:
77
In [34]:
num_features_str = ''
for ix, x in enumerate(num_vars):
    if ix == len(num_vars) - 1:
        num_features_str = num_features_str + x
    else:
        num_features_str = num_features_str + x + ' + '
num_features_str
Out[34]:
'total_ms_tp000_sqrt + mw_tp000_sqrt + mwc_tp000_sqrt + mcl_tp000_sqrt + mcr_tp000_sqrt + mm_tp000_sqrt + ks_tp000_sqrt + total_ms_tp010_sqrt + mw_tp010_sqrt + mwc_tp010_sqrt + mcl_tp010_sqrt + mcr_tp010_sqrt + mm_tp010_sqrt + ks_tp010_sqrt + total_ms_tp020_sqrt + mw_tp020_sqrt + mwc_tp020_sqrt + mcl_tp020_sqrt + mcr_tp020_sqrt + mm_tp020_sqrt + ks_tp020_sqrt + total_ms_tp030_sqrt + mw_tp030_sqrt + mwc_tp030_sqrt + mcl_tp030_sqrt + mcr_tp030_sqrt + mm_tp030_sqrt + ks_tp030_sqrt + total_ms_tp040_sqrt + mw_tp040_sqrt + mwc_tp040_sqrt + mcl_tp040_sqrt + mcr_tp040_sqrt + mm_tp040_sqrt + ks_tp040_sqrt + total_ms_tp050_sqrt + mw_tp050_sqrt + mwc_tp050_sqrt + mcl_tp050_sqrt + mcr_tp050_sqrt + mm_tp050_sqrt + ks_tp050_sqrt + total_ms_tp060_sqrt + mw_tp060_sqrt + mwc_tp060_sqrt + mcl_tp060_sqrt + mcr_tp060_sqrt + mm_tp060_sqrt + ks_tp060_sqrt + total_ms_tp070_sqrt + mw_tp070_sqrt + mwc_tp070_sqrt + mcl_tp070_sqrt + mcr_tp070_sqrt + mm_tp070_sqrt + ks_tp070_sqrt + total_ms_tp080_sqrt + mw_tp080_sqrt + mwc_tp080_sqrt + mcl_tp080_sqrt + mcr_tp080_sqrt + mm_tp080_sqrt + ks_tp080_sqrt + total_ms_tp090_sqrt + mw_tp090_sqrt + mwc_tp090_sqrt + mcl_tp090_sqrt + mcr_tp090_sqrt + mm_tp090_sqrt + ks_tp090_sqrt + total_ms_tp100_sqrt + mw_tp100_sqrt + mwc_tp100_sqrt + mcl_tp100_sqrt + mcr_tp100_sqrt + mm_tp100_sqrt + ks_tp100_sqrt'
In [35]:
descriptive_formulas = ['interim_scr ~ sid',
                    'interim_scr ~ sid + actv_grp',
                    'interim_scr ~ sid + actv_grp + ' + num_features_str,
                    'interim_scr ~ sid * (' + num_features_str + ')',
                    'interim_scr ~ sid * (actv_grp + ' + num_features_str + ')']
In [36]:
predictive_formulas = ['interim_scr ~ ' + num_features_str,
                    'interim_scr ~ (' + num_features_str + ')**2',
                    'interim_scr ~ actv_grp + ' + num_features_str,
                    'interim_scr ~ actv_grp * (' + num_features_str + ')',
                    'interim_scr ~ actv_grp + (' + num_features_str + ')**2',
                     'interim_scr ~ actv_grp * (' + num_features_str + ')**2']
In [37]:
formula_list = descriptive_formulas + predictive_formulas
In [38]:
formula_list
Out[38]:
['interim_scr ~ sid',
 'interim_scr ~ sid + actv_grp',
 'interim_scr ~ sid + actv_grp + total_ms_tp000_sqrt + mw_tp000_sqrt + mwc_tp000_sqrt + mcl_tp000_sqrt + mcr_tp000_sqrt + mm_tp000_sqrt + ks_tp000_sqrt + total_ms_tp010_sqrt + mw_tp010_sqrt + mwc_tp010_sqrt + mcl_tp010_sqrt + mcr_tp010_sqrt + mm_tp010_sqrt + ks_tp010_sqrt + total_ms_tp020_sqrt + mw_tp020_sqrt + mwc_tp020_sqrt + mcl_tp020_sqrt + mcr_tp020_sqrt + mm_tp020_sqrt + ks_tp020_sqrt + total_ms_tp030_sqrt + mw_tp030_sqrt + mwc_tp030_sqrt + mcl_tp030_sqrt + mcr_tp030_sqrt + mm_tp030_sqrt + ks_tp030_sqrt + total_ms_tp040_sqrt + mw_tp040_sqrt + mwc_tp040_sqrt + mcl_tp040_sqrt + mcr_tp040_sqrt + mm_tp040_sqrt + ks_tp040_sqrt + total_ms_tp050_sqrt + mw_tp050_sqrt + mwc_tp050_sqrt + mcl_tp050_sqrt + mcr_tp050_sqrt + mm_tp050_sqrt + ks_tp050_sqrt + total_ms_tp060_sqrt + mw_tp060_sqrt + mwc_tp060_sqrt + mcl_tp060_sqrt + mcr_tp060_sqrt + mm_tp060_sqrt + ks_tp060_sqrt + total_ms_tp070_sqrt + mw_tp070_sqrt + mwc_tp070_sqrt + mcl_tp070_sqrt + mcr_tp070_sqrt + mm_tp070_sqrt + ks_tp070_sqrt + total_ms_tp080_sqrt + mw_tp080_sqrt + mwc_tp080_sqrt + mcl_tp080_sqrt + mcr_tp080_sqrt + mm_tp080_sqrt + ks_tp080_sqrt + total_ms_tp090_sqrt + mw_tp090_sqrt + mwc_tp090_sqrt + mcl_tp090_sqrt + mcr_tp090_sqrt + mm_tp090_sqrt + ks_tp090_sqrt + total_ms_tp100_sqrt + mw_tp100_sqrt + mwc_tp100_sqrt + mcl_tp100_sqrt + mcr_tp100_sqrt + mm_tp100_sqrt + ks_tp100_sqrt',
 'interim_scr ~ sid * (total_ms_tp000_sqrt + mw_tp000_sqrt + mwc_tp000_sqrt + mcl_tp000_sqrt + mcr_tp000_sqrt + mm_tp000_sqrt + ks_tp000_sqrt + total_ms_tp010_sqrt + mw_tp010_sqrt + mwc_tp010_sqrt + mcl_tp010_sqrt + mcr_tp010_sqrt + mm_tp010_sqrt + ks_tp010_sqrt + total_ms_tp020_sqrt + mw_tp020_sqrt + mwc_tp020_sqrt + mcl_tp020_sqrt + mcr_tp020_sqrt + mm_tp020_sqrt + ks_tp020_sqrt + total_ms_tp030_sqrt + mw_tp030_sqrt + mwc_tp030_sqrt + mcl_tp030_sqrt + mcr_tp030_sqrt + mm_tp030_sqrt + ks_tp030_sqrt + total_ms_tp040_sqrt + mw_tp040_sqrt + mwc_tp040_sqrt + mcl_tp040_sqrt + mcr_tp040_sqrt + mm_tp040_sqrt + ks_tp040_sqrt + total_ms_tp050_sqrt + mw_tp050_sqrt + mwc_tp050_sqrt + mcl_tp050_sqrt + mcr_tp050_sqrt + mm_tp050_sqrt + ks_tp050_sqrt + total_ms_tp060_sqrt + mw_tp060_sqrt + mwc_tp060_sqrt + mcl_tp060_sqrt + mcr_tp060_sqrt + mm_tp060_sqrt + ks_tp060_sqrt + total_ms_tp070_sqrt + mw_tp070_sqrt + mwc_tp070_sqrt + mcl_tp070_sqrt + mcr_tp070_sqrt + mm_tp070_sqrt + ks_tp070_sqrt + total_ms_tp080_sqrt + mw_tp080_sqrt + mwc_tp080_sqrt + mcl_tp080_sqrt + mcr_tp080_sqrt + mm_tp080_sqrt + ks_tp080_sqrt + total_ms_tp090_sqrt + mw_tp090_sqrt + mwc_tp090_sqrt + mcl_tp090_sqrt + mcr_tp090_sqrt + mm_tp090_sqrt + ks_tp090_sqrt + total_ms_tp100_sqrt + mw_tp100_sqrt + mwc_tp100_sqrt + mcl_tp100_sqrt + mcr_tp100_sqrt + mm_tp100_sqrt + ks_tp100_sqrt)',
 'interim_scr ~ sid * (actv_grp + total_ms_tp000_sqrt + mw_tp000_sqrt + mwc_tp000_sqrt + mcl_tp000_sqrt + mcr_tp000_sqrt + mm_tp000_sqrt + ks_tp000_sqrt + total_ms_tp010_sqrt + mw_tp010_sqrt + mwc_tp010_sqrt + mcl_tp010_sqrt + mcr_tp010_sqrt + mm_tp010_sqrt + ks_tp010_sqrt + total_ms_tp020_sqrt + mw_tp020_sqrt + mwc_tp020_sqrt + mcl_tp020_sqrt + mcr_tp020_sqrt + mm_tp020_sqrt + ks_tp020_sqrt + total_ms_tp030_sqrt + mw_tp030_sqrt + mwc_tp030_sqrt + mcl_tp030_sqrt + mcr_tp030_sqrt + mm_tp030_sqrt + ks_tp030_sqrt + total_ms_tp040_sqrt + mw_tp040_sqrt + mwc_tp040_sqrt + mcl_tp040_sqrt + mcr_tp040_sqrt + mm_tp040_sqrt + ks_tp040_sqrt + total_ms_tp050_sqrt + mw_tp050_sqrt + mwc_tp050_sqrt + mcl_tp050_sqrt + mcr_tp050_sqrt + mm_tp050_sqrt + ks_tp050_sqrt + total_ms_tp060_sqrt + mw_tp060_sqrt + mwc_tp060_sqrt + mcl_tp060_sqrt + mcr_tp060_sqrt + mm_tp060_sqrt + ks_tp060_sqrt + total_ms_tp070_sqrt + mw_tp070_sqrt + mwc_tp070_sqrt + mcl_tp070_sqrt + mcr_tp070_sqrt + mm_tp070_sqrt + ks_tp070_sqrt + total_ms_tp080_sqrt + mw_tp080_sqrt + mwc_tp080_sqrt + mcl_tp080_sqrt + mcr_tp080_sqrt + mm_tp080_sqrt + ks_tp080_sqrt + total_ms_tp090_sqrt + mw_tp090_sqrt + mwc_tp090_sqrt + mcl_tp090_sqrt + mcr_tp090_sqrt + mm_tp090_sqrt + ks_tp090_sqrt + total_ms_tp100_sqrt + mw_tp100_sqrt + mwc_tp100_sqrt + mcl_tp100_sqrt + mcr_tp100_sqrt + mm_tp100_sqrt + ks_tp100_sqrt)',
 'interim_scr ~ total_ms_tp000_sqrt + mw_tp000_sqrt + mwc_tp000_sqrt + mcl_tp000_sqrt + mcr_tp000_sqrt + mm_tp000_sqrt + ks_tp000_sqrt + total_ms_tp010_sqrt + mw_tp010_sqrt + mwc_tp010_sqrt + mcl_tp010_sqrt + mcr_tp010_sqrt + mm_tp010_sqrt + ks_tp010_sqrt + total_ms_tp020_sqrt + mw_tp020_sqrt + mwc_tp020_sqrt + mcl_tp020_sqrt + mcr_tp020_sqrt + mm_tp020_sqrt + ks_tp020_sqrt + total_ms_tp030_sqrt + mw_tp030_sqrt + mwc_tp030_sqrt + mcl_tp030_sqrt + mcr_tp030_sqrt + mm_tp030_sqrt + ks_tp030_sqrt + total_ms_tp040_sqrt + mw_tp040_sqrt + mwc_tp040_sqrt + mcl_tp040_sqrt + mcr_tp040_sqrt + mm_tp040_sqrt + ks_tp040_sqrt + total_ms_tp050_sqrt + mw_tp050_sqrt + mwc_tp050_sqrt + mcl_tp050_sqrt + mcr_tp050_sqrt + mm_tp050_sqrt + ks_tp050_sqrt + total_ms_tp060_sqrt + mw_tp060_sqrt + mwc_tp060_sqrt + mcl_tp060_sqrt + mcr_tp060_sqrt + mm_tp060_sqrt + ks_tp060_sqrt + total_ms_tp070_sqrt + mw_tp070_sqrt + mwc_tp070_sqrt + mcl_tp070_sqrt + mcr_tp070_sqrt + mm_tp070_sqrt + ks_tp070_sqrt + total_ms_tp080_sqrt + mw_tp080_sqrt + mwc_tp080_sqrt + mcl_tp080_sqrt + mcr_tp080_sqrt + mm_tp080_sqrt + ks_tp080_sqrt + total_ms_tp090_sqrt + mw_tp090_sqrt + mwc_tp090_sqrt + mcl_tp090_sqrt + mcr_tp090_sqrt + mm_tp090_sqrt + ks_tp090_sqrt + total_ms_tp100_sqrt + mw_tp100_sqrt + mwc_tp100_sqrt + mcl_tp100_sqrt + mcr_tp100_sqrt + mm_tp100_sqrt + ks_tp100_sqrt',
 'interim_scr ~ (total_ms_tp000_sqrt + mw_tp000_sqrt + mwc_tp000_sqrt + mcl_tp000_sqrt + mcr_tp000_sqrt + mm_tp000_sqrt + ks_tp000_sqrt + total_ms_tp010_sqrt + mw_tp010_sqrt + mwc_tp010_sqrt + mcl_tp010_sqrt + mcr_tp010_sqrt + mm_tp010_sqrt + ks_tp010_sqrt + total_ms_tp020_sqrt + mw_tp020_sqrt + mwc_tp020_sqrt + mcl_tp020_sqrt + mcr_tp020_sqrt + mm_tp020_sqrt + ks_tp020_sqrt + total_ms_tp030_sqrt + mw_tp030_sqrt + mwc_tp030_sqrt + mcl_tp030_sqrt + mcr_tp030_sqrt + mm_tp030_sqrt + ks_tp030_sqrt + total_ms_tp040_sqrt + mw_tp040_sqrt + mwc_tp040_sqrt + mcl_tp040_sqrt + mcr_tp040_sqrt + mm_tp040_sqrt + ks_tp040_sqrt + total_ms_tp050_sqrt + mw_tp050_sqrt + mwc_tp050_sqrt + mcl_tp050_sqrt + mcr_tp050_sqrt + mm_tp050_sqrt + ks_tp050_sqrt + total_ms_tp060_sqrt + mw_tp060_sqrt + mwc_tp060_sqrt + mcl_tp060_sqrt + mcr_tp060_sqrt + mm_tp060_sqrt + ks_tp060_sqrt + total_ms_tp070_sqrt + mw_tp070_sqrt + mwc_tp070_sqrt + mcl_tp070_sqrt + mcr_tp070_sqrt + mm_tp070_sqrt + ks_tp070_sqrt + total_ms_tp080_sqrt + mw_tp080_sqrt + mwc_tp080_sqrt + mcl_tp080_sqrt + mcr_tp080_sqrt + mm_tp080_sqrt + ks_tp080_sqrt + total_ms_tp090_sqrt + mw_tp090_sqrt + mwc_tp090_sqrt + mcl_tp090_sqrt + mcr_tp090_sqrt + mm_tp090_sqrt + ks_tp090_sqrt + total_ms_tp100_sqrt + mw_tp100_sqrt + mwc_tp100_sqrt + mcl_tp100_sqrt + mcr_tp100_sqrt + mm_tp100_sqrt + ks_tp100_sqrt)**2',
 'interim_scr ~ actv_grp + total_ms_tp000_sqrt + mw_tp000_sqrt + mwc_tp000_sqrt + mcl_tp000_sqrt + mcr_tp000_sqrt + mm_tp000_sqrt + ks_tp000_sqrt + total_ms_tp010_sqrt + mw_tp010_sqrt + mwc_tp010_sqrt + mcl_tp010_sqrt + mcr_tp010_sqrt + mm_tp010_sqrt + ks_tp010_sqrt + total_ms_tp020_sqrt + mw_tp020_sqrt + mwc_tp020_sqrt + mcl_tp020_sqrt + mcr_tp020_sqrt + mm_tp020_sqrt + ks_tp020_sqrt + total_ms_tp030_sqrt + mw_tp030_sqrt + mwc_tp030_sqrt + mcl_tp030_sqrt + mcr_tp030_sqrt + mm_tp030_sqrt + ks_tp030_sqrt + total_ms_tp040_sqrt + mw_tp040_sqrt + mwc_tp040_sqrt + mcl_tp040_sqrt + mcr_tp040_sqrt + mm_tp040_sqrt + ks_tp040_sqrt + total_ms_tp050_sqrt + mw_tp050_sqrt + mwc_tp050_sqrt + mcl_tp050_sqrt + mcr_tp050_sqrt + mm_tp050_sqrt + ks_tp050_sqrt + total_ms_tp060_sqrt + mw_tp060_sqrt + mwc_tp060_sqrt + mcl_tp060_sqrt + mcr_tp060_sqrt + mm_tp060_sqrt + ks_tp060_sqrt + total_ms_tp070_sqrt + mw_tp070_sqrt + mwc_tp070_sqrt + mcl_tp070_sqrt + mcr_tp070_sqrt + mm_tp070_sqrt + ks_tp070_sqrt + total_ms_tp080_sqrt + mw_tp080_sqrt + mwc_tp080_sqrt + mcl_tp080_sqrt + mcr_tp080_sqrt + mm_tp080_sqrt + ks_tp080_sqrt + total_ms_tp090_sqrt + mw_tp090_sqrt + mwc_tp090_sqrt + mcl_tp090_sqrt + mcr_tp090_sqrt + mm_tp090_sqrt + ks_tp090_sqrt + total_ms_tp100_sqrt + mw_tp100_sqrt + mwc_tp100_sqrt + mcl_tp100_sqrt + mcr_tp100_sqrt + mm_tp100_sqrt + ks_tp100_sqrt',
 'interim_scr ~ actv_grp * (total_ms_tp000_sqrt + mw_tp000_sqrt + mwc_tp000_sqrt + mcl_tp000_sqrt + mcr_tp000_sqrt + mm_tp000_sqrt + ks_tp000_sqrt + total_ms_tp010_sqrt + mw_tp010_sqrt + mwc_tp010_sqrt + mcl_tp010_sqrt + mcr_tp010_sqrt + mm_tp010_sqrt + ks_tp010_sqrt + total_ms_tp020_sqrt + mw_tp020_sqrt + mwc_tp020_sqrt + mcl_tp020_sqrt + mcr_tp020_sqrt + mm_tp020_sqrt + ks_tp020_sqrt + total_ms_tp030_sqrt + mw_tp030_sqrt + mwc_tp030_sqrt + mcl_tp030_sqrt + mcr_tp030_sqrt + mm_tp030_sqrt + ks_tp030_sqrt + total_ms_tp040_sqrt + mw_tp040_sqrt + mwc_tp040_sqrt + mcl_tp040_sqrt + mcr_tp040_sqrt + mm_tp040_sqrt + ks_tp040_sqrt + total_ms_tp050_sqrt + mw_tp050_sqrt + mwc_tp050_sqrt + mcl_tp050_sqrt + mcr_tp050_sqrt + mm_tp050_sqrt + ks_tp050_sqrt + total_ms_tp060_sqrt + mw_tp060_sqrt + mwc_tp060_sqrt + mcl_tp060_sqrt + mcr_tp060_sqrt + mm_tp060_sqrt + ks_tp060_sqrt + total_ms_tp070_sqrt + mw_tp070_sqrt + mwc_tp070_sqrt + mcl_tp070_sqrt + mcr_tp070_sqrt + mm_tp070_sqrt + ks_tp070_sqrt + total_ms_tp080_sqrt + mw_tp080_sqrt + mwc_tp080_sqrt + mcl_tp080_sqrt + mcr_tp080_sqrt + mm_tp080_sqrt + ks_tp080_sqrt + total_ms_tp090_sqrt + mw_tp090_sqrt + mwc_tp090_sqrt + mcl_tp090_sqrt + mcr_tp090_sqrt + mm_tp090_sqrt + ks_tp090_sqrt + total_ms_tp100_sqrt + mw_tp100_sqrt + mwc_tp100_sqrt + mcl_tp100_sqrt + mcr_tp100_sqrt + mm_tp100_sqrt + ks_tp100_sqrt)',
 'interim_scr ~ actv_grp + (total_ms_tp000_sqrt + mw_tp000_sqrt + mwc_tp000_sqrt + mcl_tp000_sqrt + mcr_tp000_sqrt + mm_tp000_sqrt + ks_tp000_sqrt + total_ms_tp010_sqrt + mw_tp010_sqrt + mwc_tp010_sqrt + mcl_tp010_sqrt + mcr_tp010_sqrt + mm_tp010_sqrt + ks_tp010_sqrt + total_ms_tp020_sqrt + mw_tp020_sqrt + mwc_tp020_sqrt + mcl_tp020_sqrt + mcr_tp020_sqrt + mm_tp020_sqrt + ks_tp020_sqrt + total_ms_tp030_sqrt + mw_tp030_sqrt + mwc_tp030_sqrt + mcl_tp030_sqrt + mcr_tp030_sqrt + mm_tp030_sqrt + ks_tp030_sqrt + total_ms_tp040_sqrt + mw_tp040_sqrt + mwc_tp040_sqrt + mcl_tp040_sqrt + mcr_tp040_sqrt + mm_tp040_sqrt + ks_tp040_sqrt + total_ms_tp050_sqrt + mw_tp050_sqrt + mwc_tp050_sqrt + mcl_tp050_sqrt + mcr_tp050_sqrt + mm_tp050_sqrt + ks_tp050_sqrt + total_ms_tp060_sqrt + mw_tp060_sqrt + mwc_tp060_sqrt + mcl_tp060_sqrt + mcr_tp060_sqrt + mm_tp060_sqrt + ks_tp060_sqrt + total_ms_tp070_sqrt + mw_tp070_sqrt + mwc_tp070_sqrt + mcl_tp070_sqrt + mcr_tp070_sqrt + mm_tp070_sqrt + ks_tp070_sqrt + total_ms_tp080_sqrt + mw_tp080_sqrt + mwc_tp080_sqrt + mcl_tp080_sqrt + mcr_tp080_sqrt + mm_tp080_sqrt + ks_tp080_sqrt + total_ms_tp090_sqrt + mw_tp090_sqrt + mwc_tp090_sqrt + mcl_tp090_sqrt + mcr_tp090_sqrt + mm_tp090_sqrt + ks_tp090_sqrt + total_ms_tp100_sqrt + mw_tp100_sqrt + mwc_tp100_sqrt + mcl_tp100_sqrt + mcr_tp100_sqrt + mm_tp100_sqrt + ks_tp100_sqrt)**2',
 'interim_scr ~ actv_grp * (total_ms_tp000_sqrt + mw_tp000_sqrt + mwc_tp000_sqrt + mcl_tp000_sqrt + mcr_tp000_sqrt + mm_tp000_sqrt + ks_tp000_sqrt + total_ms_tp010_sqrt + mw_tp010_sqrt + mwc_tp010_sqrt + mcl_tp010_sqrt + mcr_tp010_sqrt + mm_tp010_sqrt + ks_tp010_sqrt + total_ms_tp020_sqrt + mw_tp020_sqrt + mwc_tp020_sqrt + mcl_tp020_sqrt + mcr_tp020_sqrt + mm_tp020_sqrt + ks_tp020_sqrt + total_ms_tp030_sqrt + mw_tp030_sqrt + mwc_tp030_sqrt + mcl_tp030_sqrt + mcr_tp030_sqrt + mm_tp030_sqrt + ks_tp030_sqrt + total_ms_tp040_sqrt + mw_tp040_sqrt + mwc_tp040_sqrt + mcl_tp040_sqrt + mcr_tp040_sqrt + mm_tp040_sqrt + ks_tp040_sqrt + total_ms_tp050_sqrt + mw_tp050_sqrt + mwc_tp050_sqrt + mcl_tp050_sqrt + mcr_tp050_sqrt + mm_tp050_sqrt + ks_tp050_sqrt + total_ms_tp060_sqrt + mw_tp060_sqrt + mwc_tp060_sqrt + mcl_tp060_sqrt + mcr_tp060_sqrt + mm_tp060_sqrt + ks_tp060_sqrt + total_ms_tp070_sqrt + mw_tp070_sqrt + mwc_tp070_sqrt + mcl_tp070_sqrt + mcr_tp070_sqrt + mm_tp070_sqrt + ks_tp070_sqrt + total_ms_tp080_sqrt + mw_tp080_sqrt + mwc_tp080_sqrt + mcl_tp080_sqrt + mcr_tp080_sqrt + mm_tp080_sqrt + ks_tp080_sqrt + total_ms_tp090_sqrt + mw_tp090_sqrt + mwc_tp090_sqrt + mcl_tp090_sqrt + mcr_tp090_sqrt + mm_tp090_sqrt + ks_tp090_sqrt + total_ms_tp100_sqrt + mw_tp100_sqrt + mwc_tp100_sqrt + mcl_tp100_sqrt + mcr_tp100_sqrt + mm_tp100_sqrt + ks_tp100_sqrt)**2']
In [39]:
complx_model = formula_list[10]
complx_model
Out[39]:
'interim_scr ~ actv_grp * (total_ms_tp000_sqrt + mw_tp000_sqrt + mwc_tp000_sqrt + mcl_tp000_sqrt + mcr_tp000_sqrt + mm_tp000_sqrt + ks_tp000_sqrt + total_ms_tp010_sqrt + mw_tp010_sqrt + mwc_tp010_sqrt + mcl_tp010_sqrt + mcr_tp010_sqrt + mm_tp010_sqrt + ks_tp010_sqrt + total_ms_tp020_sqrt + mw_tp020_sqrt + mwc_tp020_sqrt + mcl_tp020_sqrt + mcr_tp020_sqrt + mm_tp020_sqrt + ks_tp020_sqrt + total_ms_tp030_sqrt + mw_tp030_sqrt + mwc_tp030_sqrt + mcl_tp030_sqrt + mcr_tp030_sqrt + mm_tp030_sqrt + ks_tp030_sqrt + total_ms_tp040_sqrt + mw_tp040_sqrt + mwc_tp040_sqrt + mcl_tp040_sqrt + mcr_tp040_sqrt + mm_tp040_sqrt + ks_tp040_sqrt + total_ms_tp050_sqrt + mw_tp050_sqrt + mwc_tp050_sqrt + mcl_tp050_sqrt + mcr_tp050_sqrt + mm_tp050_sqrt + ks_tp050_sqrt + total_ms_tp060_sqrt + mw_tp060_sqrt + mwc_tp060_sqrt + mcl_tp060_sqrt + mcr_tp060_sqrt + mm_tp060_sqrt + ks_tp060_sqrt + total_ms_tp070_sqrt + mw_tp070_sqrt + mwc_tp070_sqrt + mcl_tp070_sqrt + mcr_tp070_sqrt + mm_tp070_sqrt + ks_tp070_sqrt + total_ms_tp080_sqrt + mw_tp080_sqrt + mwc_tp080_sqrt + mcl_tp080_sqrt + mcr_tp080_sqrt + mm_tp080_sqrt + ks_tp080_sqrt + total_ms_tp090_sqrt + mw_tp090_sqrt + mwc_tp090_sqrt + mcl_tp090_sqrt + mcr_tp090_sqrt + mm_tp090_sqrt + ks_tp090_sqrt + total_ms_tp100_sqrt + mw_tp100_sqrt + mwc_tp100_sqrt + mcl_tp100_sqrt + mcr_tp100_sqrt + mm_tp100_sqrt + ks_tp100_sqrt)**2'

Evaluate formula features¶

In [40]:
def make_dmat(df, formula_list):
    
    sk_list = []

    for a_formula in formula_list:
        y_sk, X_sk = dmatrices(a_formula, data = df)
        sk_list.append( [y_sk, X_sk] )
        
    return sk_list
In [41]:
def make_dim_df(df, sk_list, formula_list):
        
    model_dim = pd.DataFrame({'model name': [x for x in range(0,len(formula_list))],
                          'dimensions': [dim[1].shape[1] for dim in sk_list],
                          'number of obs': [len(df) for x in range(0,len(formula_list))],
                          'dim < obs': ['Yes' if dim[1].shape[1] < len(df) else 'No' for dim in sk_list]})
    return model_dim
Session 2¶
In [42]:
s2_df = io_df[ io_df['sess'] == 2 ].copy()
In [43]:
s2_df
Out[43]:
sess sid actv_grp total_ms_tp000_sqrt mw_tp000_sqrt mwc_tp000_sqrt mcl_tp000_sqrt mcr_tp000_sqrt mm_tp000_sqrt ks_tp000_sqrt ... mm_tp090_sqrt ks_tp090_sqrt total_ms_tp100_sqrt mw_tp100_sqrt mwc_tp100_sqrt mcl_tp100_sqrt mcr_tp100_sqrt mm_tp100_sqrt ks_tp100_sqrt interim_scr
606 2 1 Aulaweb 1236.122971 16.643317 0.0 25.278449 1.414214 224.784341 37.496667 ... 486.501593 51.314715 2760.796986 37.775654 0.0 61.212744 16.309506 520.037499 54.387499 5.0
607 2 1 Blank 216.794834 2.645751 0.0 4.582576 0.000000 46.808119 2.828427 ... 494.317509 52.801515 2930.699575 38.483763 0.0 65.069194 17.720045 550.932845 57.113921 5.0
608 2 1 Deeds 70.710678 0.000000 0.0 2.449490 0.000000 21.260292 0.000000 ... 501.163047 54.166410 2928.310093 38.470768 0.0 64.992307 17.720045 550.207234 56.920998 5.0
609 2 1 Diagram 604.979338 4.472136 0.0 14.832397 0.000000 117.085439 14.352700 ... 525.389950 54.896266 2927.968579 38.470768 0.0 64.946132 17.720045 549.960908 56.920998 5.0
610 2 1 Other 771.362431 4.472136 0.0 16.852300 0.000000 151.650915 14.352700 ... 521.050669 54.721111 2933.087111 38.483763 0.0 65.306967 17.720045 552.080610 57.410800 5.0
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
1254 2 104 Diagram 412.310563 3.464102 0.0 11.747340 0.000000 74.959989 15.874508 ... 381.201522 59.841457 2703.146315 24.839485 0.0 55.587768 7.615773 412.372405 63.929649 6.0
1255 2 104 Other 134.164079 1.732051 0.0 1.414214 0.000000 23.151674 0.000000 ... 417.693309 64.023433 2738.795356 29.478806 0.0 56.480085 7.745967 419.435335 64.474801 6.0
1256 2 104 Properties 800.000000 12.206556 0.0 18.000000 2.000000 151.367103 27.294688 ... 247.365721 36.573214 2688.308018 24.062419 0.0 54.808758 7.615773 407.839429 63.545259 6.0
1257 2 104 Study 404.969135 3.464102 0.0 11.401754 0.000000 71.798329 15.874508 ... 384.790852 59.874870 2712.747685 25.592968 0.0 55.677644 7.615773 413.134361 63.929649 6.0
1258 2 104 TextEditor 141.421356 2.449490 0.0 2.000000 0.000000 25.219040 0.000000 ... 414.130414 63.929649 2733.130074 29.478806 0.0 56.409219 7.615773 418.615575 64.023433 6.0

653 rows × 81 columns

In [44]:
sk_s2_list = make_dmat(s2_df, formula_list)
In [ ]:
In [45]:
model_dim_s2 = make_dim_df(s2_df, sk_s2_list, formula_list)
In [46]:
model_dim_s2
Out[46]:
model name dimensions number of obs dim < obs
0 0 81 653 Yes
1 1 90 653 Yes
2 2 167 653 Yes
3 3 6318 653 No
4 4 7047 653 No
5 5 78 653 Yes
6 6 3004 653 No
7 7 87 653 Yes
8 8 780 653 No
9 9 3013 653 No
10 10 30040 653 No
Session 3¶
In [47]:
s3_df = io_df[ io_df['sess'] == 3 ].copy()
In [48]:
sk_s3_list = make_dmat(s3_df, formula_list)
In [49]:
model_dim_s3 = make_dim_df(s3_df, sk_s3_list, formula_list)
In [50]:
model_dim_s3
Out[50]:
model name dimensions number of obs dim < obs
0 0 86 684 Yes
1 1 95 684 Yes
2 2 172 684 Yes
3 3 6708 684 No
4 4 7482 684 No
5 5 78 684 Yes
6 6 3004 684 No
7 7 87 684 Yes
8 8 780 684 No
9 9 3013 684 No
10 10 30040 684 No
Session 4¶
In [51]:
s4_df = io_df[ io_df['sess'] == 4 ].copy()
In [52]:
sk_s4_list = make_dmat(s4_df, formula_list)
In [53]:
model_dim_s4 = make_dim_df(s4_df, sk_s4_list, formula_list)
In [54]:
model_dim_s4
Out[54]:
model name dimensions number of obs dim < obs
0 0 98 766 Yes
1 1 107 766 Yes
2 2 184 766 Yes
3 3 7644 766 No
4 4 8526 766 No
5 5 78 766 Yes
6 6 3004 766 No
7 7 87 766 Yes
8 8 780 766 No
9 9 3013 766 No
10 10 30040 766 No
Session 5¶
In [55]:
s5_df = io_df[ io_df['sess'] == 5 ].copy()
In [56]:
sk_s5_list = make_dmat(s5_df, formula_list)
In [57]:
model_dim_s5 = make_dim_df(s5_df, sk_s5_list, formula_list)
In [58]:
model_dim_s5
Out[58]:
model name dimensions number of obs dim < obs
0 0 90 721 Yes
1 1 99 721 Yes
2 2 176 721 Yes
3 3 7020 721 No
4 4 7830 721 No
5 5 78 721 Yes
6 6 3004 721 No
7 7 87 721 Yes
8 8 780 721 No
9 9 3013 721 No
10 10 30040 721 No
Session 6¶
In [59]:
s6_df = io_df[ io_df['sess'] == 6 ].copy()
In [60]:
sk_s6_list = make_dmat(s6_df, formula_list)
In [61]:
model_dim_s6 = make_dim_df(s6_df, sk_s6_list, formula_list)
In [62]:
model_dim_s6
Out[62]:
model name dimensions number of obs dim < obs
0 0 83 818 Yes
1 1 93 818 Yes
2 2 170 818 Yes
3 3 6474 818 No
4 4 7304 818 No
5 5 78 818 Yes
6 6 3004 818 No
7 7 88 818 Yes
8 8 858 818 No
9 9 3014 818 No
10 10 33044 818 No

Visualize the numeric inputs per session¶

In [63]:
num_vars
Out[63]:
['total_ms_tp000_sqrt',
 'mw_tp000_sqrt',
 'mwc_tp000_sqrt',
 'mcl_tp000_sqrt',
 'mcr_tp000_sqrt',
 'mm_tp000_sqrt',
 'ks_tp000_sqrt',
 'total_ms_tp010_sqrt',
 'mw_tp010_sqrt',
 'mwc_tp010_sqrt',
 'mcl_tp010_sqrt',
 'mcr_tp010_sqrt',
 'mm_tp010_sqrt',
 'ks_tp010_sqrt',
 'total_ms_tp020_sqrt',
 'mw_tp020_sqrt',
 'mwc_tp020_sqrt',
 'mcl_tp020_sqrt',
 'mcr_tp020_sqrt',
 'mm_tp020_sqrt',
 'ks_tp020_sqrt',
 'total_ms_tp030_sqrt',
 'mw_tp030_sqrt',
 'mwc_tp030_sqrt',
 'mcl_tp030_sqrt',
 'mcr_tp030_sqrt',
 'mm_tp030_sqrt',
 'ks_tp030_sqrt',
 'total_ms_tp040_sqrt',
 'mw_tp040_sqrt',
 'mwc_tp040_sqrt',
 'mcl_tp040_sqrt',
 'mcr_tp040_sqrt',
 'mm_tp040_sqrt',
 'ks_tp040_sqrt',
 'total_ms_tp050_sqrt',
 'mw_tp050_sqrt',
 'mwc_tp050_sqrt',
 'mcl_tp050_sqrt',
 'mcr_tp050_sqrt',
 'mm_tp050_sqrt',
 'ks_tp050_sqrt',
 'total_ms_tp060_sqrt',
 'mw_tp060_sqrt',
 'mwc_tp060_sqrt',
 'mcl_tp060_sqrt',
 'mcr_tp060_sqrt',
 'mm_tp060_sqrt',
 'ks_tp060_sqrt',
 'total_ms_tp070_sqrt',
 'mw_tp070_sqrt',
 'mwc_tp070_sqrt',
 'mcl_tp070_sqrt',
 'mcr_tp070_sqrt',
 'mm_tp070_sqrt',
 'ks_tp070_sqrt',
 'total_ms_tp080_sqrt',
 'mw_tp080_sqrt',
 'mwc_tp080_sqrt',
 'mcl_tp080_sqrt',
 'mcr_tp080_sqrt',
 'mm_tp080_sqrt',
 'ks_tp080_sqrt',
 'total_ms_tp090_sqrt',
 'mw_tp090_sqrt',
 'mwc_tp090_sqrt',
 'mcl_tp090_sqrt',
 'mcr_tp090_sqrt',
 'mm_tp090_sqrt',
 'ks_tp090_sqrt',
 'total_ms_tp100_sqrt',
 'mw_tp100_sqrt',
 'mwc_tp100_sqrt',
 'mcl_tp100_sqrt',
 'mcr_tp100_sqrt',
 'mm_tp100_sqrt',
 'ks_tp100_sqrt']
Session 2¶
In [64]:
sns.catplot(data = s2_df.loc[:, num_vars], kind='box', aspect=5)

plt.show()
In [65]:
sns.displot(data = s2_df.loc[:, ['sid'] + num_vars].melt(id_vars='sid'),
            x='value', col='variable', kind='hist', bins=25,
            facet_kws={'sharex': False, 'sharey': False},
            col_wrap=5)

plt.show()
In [66]:
fig, ax = plt.subplots(figsize=(12, 8))

s2_df.loc[:, num_vars].describe().loc[['min', 'max'], :].T.plot(ax=ax)

plt.show()
In [67]:
fig, ax = plt.subplots(figsize=(12, 8))

sns.heatmap(data = s2_df.loc[:, num_vars].corr(),
            vmin=-1, vmax=1, center=0,
            cmap='coolwarm',
            ax=ax)

plt.show()
Session 3¶
In [68]:
sns.catplot(data = s3_df.loc[:, num_vars], kind='box', aspect=5)

plt.show()
In [69]:
sns.displot(data = s3_df.loc[:, ['sid'] + num_vars].melt(id_vars='sid'),
            x='value', col='variable', kind='hist', bins=25, 
            facet_kws={'sharex': False, 'sharey': False},
            col_wrap=5)

plt.show()
In [70]:
fig, ax = plt.subplots(figsize=(12, 8))

s3_df.loc[:, num_vars].describe().loc[['min', 'max'], :].T.plot(ax=ax)

plt.show()
In [71]:
fig, ax = plt.subplots(figsize=(12, 8))

sns.heatmap(data = s3_df.loc[:, num_vars].corr(),
            vmin=-1, vmax=1, center=0,
            cmap='coolwarm',
            ax=ax)

plt.show()
Session 4¶
In [72]:
sns.catplot(data = s4_df.loc[:, num_vars], kind='box', aspect=5)

plt.show()
In [73]:
sns.displot(data = s4_df.loc[:, ['sid'] + num_vars].melt(id_vars='sid'),
            x='value', col='variable', kind='hist', bins=25,
            facet_kws={'sharex': False, 'sharey': False},
            col_wrap=5)

plt.show()
In [74]:
fig, ax = plt.subplots(figsize=(12, 8))

s4_df.loc[:, num_vars].describe().loc[['min', 'max'], :].T.plot(ax=ax)

plt.show()
In [75]:
fig, ax = plt.subplots(figsize=(12, 8))

sns.heatmap(data = s4_df.loc[:, num_vars].corr(),
            vmin=-1, vmax=1, center=0,
            cmap='coolwarm',
            ax=ax)

plt.show()
Session 5¶
In [76]:
sns.catplot(data = s5_df.loc[:, num_vars], kind='box', aspect=5)

plt.show()
In [77]:
sns.displot(data = s5_df.loc[:, ['sid'] + num_vars].melt(id_vars='sid'),
            x='value', col='variable', kind='hist', bins=25,
            facet_kws={'sharex': False, 'sharey': False},
            col_wrap=5)

plt.show()
In [78]:
fig, ax = plt.subplots(figsize=(12, 8))

s5_df.loc[:, num_vars].describe().loc[['min', 'max'], :].T.plot(ax=ax)

plt.show()
In [79]:
fig, ax = plt.subplots(figsize=(12, 8))

sns.heatmap(data = s5_df.loc[:, num_vars].corr(),
            vmin=-1, vmax=1, center=0,
            cmap='coolwarm',
            ax=ax)

plt.show()
Session 6¶
In [80]:
sns.catplot(data = s6_df.loc[:, num_vars], kind='box', aspect=5)

plt.show()
In [81]:
sns.displot(data = s6_df.loc[:, ['sid'] + num_vars].melt(id_vars='sid'),
            x='value', col='variable', kind='hist', bins=25,
            facet_kws={'sharex': False, 'sharey': False},
            col_wrap=5)

plt.show()
In [82]:
fig, ax = plt.subplots(figsize=(12, 8))

s6_df.loc[:, num_vars].describe().loc[['min', 'max'], :].T.plot(ax=ax)

plt.show()
In [83]:
fig, ax = plt.subplots(figsize=(12, 8))

sns.heatmap(data = s6_df.loc[:, num_vars].corr(),
            vmin=-1, vmax=1, center=0,
            cmap='coolwarm',
            ax=ax)

plt.show()

Preprocessing with Pipelines¶

Categorical and continuous reprocessors and pipelines for additive model with pairwise interaction between continuous variables¶

The number of features between the formula interface model and the Pipelines model differs by 1 because of the intercept column of ones in the formula interface model.

In [84]:
categorical_inputs = ['actv_grp']
In [85]:
categorical_transform = Pipeline( steps = [ ('dummy', OneHotEncoder(drop='first')) ] )
In [86]:
numeric_transform_pairs = Pipeline( steps=[('std_input', StandardScaler()),
                                        ('make_poly', PolynomialFeatures(degree=2, interaction_only = True, include_bias=False))])
In [87]:
pair_transform = ColumnTransformer( transformers=[('num', numeric_transform_pairs, num_vars),
                                                    ('cat', categorical_transform, categorical_inputs)])
In [88]:
pair_transform.fit_transform( s2_df ).shape
Out[88]:
(653, 3012)
In [89]:
sk_s2_list[9][1].shape
Out[89]:
(653, 3013)

Pipelines with PCA¶

In [90]:
s2_df
Out[90]:
sess sid actv_grp total_ms_tp000_sqrt mw_tp000_sqrt mwc_tp000_sqrt mcl_tp000_sqrt mcr_tp000_sqrt mm_tp000_sqrt ks_tp000_sqrt ... mm_tp090_sqrt ks_tp090_sqrt total_ms_tp100_sqrt mw_tp100_sqrt mwc_tp100_sqrt mcl_tp100_sqrt mcr_tp100_sqrt mm_tp100_sqrt ks_tp100_sqrt interim_scr
606 2 1 Aulaweb 1236.122971 16.643317 0.0 25.278449 1.414214 224.784341 37.496667 ... 486.501593 51.314715 2760.796986 37.775654 0.0 61.212744 16.309506 520.037499 54.387499 5.0
607 2 1 Blank 216.794834 2.645751 0.0 4.582576 0.000000 46.808119 2.828427 ... 494.317509 52.801515 2930.699575 38.483763 0.0 65.069194 17.720045 550.932845 57.113921 5.0
608 2 1 Deeds 70.710678 0.000000 0.0 2.449490 0.000000 21.260292 0.000000 ... 501.163047 54.166410 2928.310093 38.470768 0.0 64.992307 17.720045 550.207234 56.920998 5.0
609 2 1 Diagram 604.979338 4.472136 0.0 14.832397 0.000000 117.085439 14.352700 ... 525.389950 54.896266 2927.968579 38.470768 0.0 64.946132 17.720045 549.960908 56.920998 5.0
610 2 1 Other 771.362431 4.472136 0.0 16.852300 0.000000 151.650915 14.352700 ... 521.050669 54.721111 2933.087111 38.483763 0.0 65.306967 17.720045 552.080610 57.410800 5.0
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
1254 2 104 Diagram 412.310563 3.464102 0.0 11.747340 0.000000 74.959989 15.874508 ... 381.201522 59.841457 2703.146315 24.839485 0.0 55.587768 7.615773 412.372405 63.929649 6.0
1255 2 104 Other 134.164079 1.732051 0.0 1.414214 0.000000 23.151674 0.000000 ... 417.693309 64.023433 2738.795356 29.478806 0.0 56.480085 7.745967 419.435335 64.474801 6.0
1256 2 104 Properties 800.000000 12.206556 0.0 18.000000 2.000000 151.367103 27.294688 ... 247.365721 36.573214 2688.308018 24.062419 0.0 54.808758 7.615773 407.839429 63.545259 6.0
1257 2 104 Study 404.969135 3.464102 0.0 11.401754 0.000000 71.798329 15.874508 ... 384.790852 59.874870 2712.747685 25.592968 0.0 55.677644 7.615773 413.134361 63.929649 6.0
1258 2 104 TextEditor 141.421356 2.449490 0.0 2.000000 0.000000 25.219040 0.000000 ... 414.130414 63.929649 2733.130074 29.478806 0.0 56.409219 7.615773 418.615575 64.023433 6.0

653 rows × 81 columns

In [91]:
x_num_only = s2_df.loc[:, num_vars].copy()
In [92]:
x_num_only.isna().sum()
Out[92]:
total_ms_tp000_sqrt    0
mw_tp000_sqrt          0
mwc_tp000_sqrt         0
mcl_tp000_sqrt         0
mcr_tp000_sqrt         0
                      ..
mwc_tp100_sqrt         0
mcl_tp100_sqrt         0
mcr_tp100_sqrt         0
mm_tp100_sqrt          0
ks_tp100_sqrt          0
Length: 77, dtype: int64
In [93]:
youtput = s2_df.loc[:, ['interim_scr']].copy()
In [94]:
numeric_transform_std = Pipeline( steps = [ ('std_input', StandardScaler()) ])
In [95]:
X_train_num_only = x_num_only.to_numpy()
In [96]:
y_train = youtput.interim_scr.to_numpy().ravel()
In [97]:
my_cv = KFold(n_splits=5, random_state=1, shuffle=True)
In [98]:
enet_default = ElasticNet(random_state=101, max_iter=100001,
                                  alpha=1.0, l1_ratio=0.5)
In [99]:
x_num_only.columns
Out[99]:
Index(['total_ms_tp000_sqrt', 'mw_tp000_sqrt', 'mwc_tp000_sqrt',
       'mcl_tp000_sqrt', 'mcr_tp000_sqrt', 'mm_tp000_sqrt', 'ks_tp000_sqrt',
       'total_ms_tp010_sqrt', 'mw_tp010_sqrt', 'mwc_tp010_sqrt',
       'mcl_tp010_sqrt', 'mcr_tp010_sqrt', 'mm_tp010_sqrt', 'ks_tp010_sqrt',
       'total_ms_tp020_sqrt', 'mw_tp020_sqrt', 'mwc_tp020_sqrt',
       'mcl_tp020_sqrt', 'mcr_tp020_sqrt', 'mm_tp020_sqrt', 'ks_tp020_sqrt',
       'total_ms_tp030_sqrt', 'mw_tp030_sqrt', 'mwc_tp030_sqrt',
       'mcl_tp030_sqrt', 'mcr_tp030_sqrt', 'mm_tp030_sqrt', 'ks_tp030_sqrt',
       'total_ms_tp040_sqrt', 'mw_tp040_sqrt', 'mwc_tp040_sqrt',
       'mcl_tp040_sqrt', 'mcr_tp040_sqrt', 'mm_tp040_sqrt', 'ks_tp040_sqrt',
       'total_ms_tp050_sqrt', 'mw_tp050_sqrt', 'mwc_tp050_sqrt',
       'mcl_tp050_sqrt', 'mcr_tp050_sqrt', 'mm_tp050_sqrt', 'ks_tp050_sqrt',
       'total_ms_tp060_sqrt', 'mw_tp060_sqrt', 'mwc_tp060_sqrt',
       'mcl_tp060_sqrt', 'mcr_tp060_sqrt', 'mm_tp060_sqrt', 'ks_tp060_sqrt',
       'total_ms_tp070_sqrt', 'mw_tp070_sqrt', 'mwc_tp070_sqrt',
       'mcl_tp070_sqrt', 'mcr_tp070_sqrt', 'mm_tp070_sqrt', 'ks_tp070_sqrt',
       'total_ms_tp080_sqrt', 'mw_tp080_sqrt', 'mwc_tp080_sqrt',
       'mcl_tp080_sqrt', 'mcr_tp080_sqrt', 'mm_tp080_sqrt', 'ks_tp080_sqrt',
       'total_ms_tp090_sqrt', 'mw_tp090_sqrt', 'mwc_tp090_sqrt',
       'mcl_tp090_sqrt', 'mcr_tp090_sqrt', 'mm_tp090_sqrt', 'ks_tp090_sqrt',
       'total_ms_tp100_sqrt', 'mw_tp100_sqrt', 'mwc_tp100_sqrt',
       'mcl_tp100_sqrt', 'mcr_tp100_sqrt', 'mm_tp100_sqrt', 'ks_tp100_sqrt'],
      dtype='object')
In [100]:
x_num_only_ready = StandardScaler().fit_transform( x_num_only )
In [101]:
pca_object = PCA().fit(x_num_only_ready)
In [102]:
pc_scores = pca_object.transform( x_num_only_ready )
PCA Correlation¶
In [103]:
fig, ax = plt.subplots(figsize=(12, 8))

sns.heatmap(pd.DataFrame(pc_scores).corr(),
           vmin=-1, vmax=1, center=0,
           cmap='coolwarm', 
           ax=ax)

plt.show()
PCA Scree plot¶
In [104]:
fig, ax = plt.subplots(figsize=(12, 8))

ax.plot( np.arange( len(pca_object.explained_variance_ratio_ ) )+1, pca_object.explained_variance_ratio_, 'bo-')

ax.set_xlabel('PC')
ax.set_ylabel('Variance Explained Ratio')

plt.show()
In [105]:
total_var_explain = pca_object.explained_variance_ratio_.cumsum()
In [106]:
fig, ax = plt.subplots(figsize=(12, 6))

ax.plot( np.arange( len(total_var_explain) ) + 1, total_var_explain, 'bo-')

ax.set_xlabel('PC')
ax.set_ylabel('Total variance explained')

plt.show()
In [107]:
pc_scores_df = pd.DataFrame( pc_scores, columns=['PC' + str(d+1).zfill(2) for d in range( pc_scores.shape[1]) ] )
In [108]:
pc_scores_df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 653 entries, 0 to 652
Data columns (total 77 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   PC01    653 non-null    float64
 1   PC02    653 non-null    float64
 2   PC03    653 non-null    float64
 3   PC04    653 non-null    float64
 4   PC05    653 non-null    float64
 5   PC06    653 non-null    float64
 6   PC07    653 non-null    float64
 7   PC08    653 non-null    float64
 8   PC09    653 non-null    float64
 9   PC10    653 non-null    float64
 10  PC11    653 non-null    float64
 11  PC12    653 non-null    float64
 12  PC13    653 non-null    float64
 13  PC14    653 non-null    float64
 14  PC15    653 non-null    float64
 15  PC16    653 non-null    float64
 16  PC17    653 non-null    float64
 17  PC18    653 non-null    float64
 18  PC19    653 non-null    float64
 19  PC20    653 non-null    float64
 20  PC21    653 non-null    float64
 21  PC22    653 non-null    float64
 22  PC23    653 non-null    float64
 23  PC24    653 non-null    float64
 24  PC25    653 non-null    float64
 25  PC26    653 non-null    float64
 26  PC27    653 non-null    float64
 27  PC28    653 non-null    float64
 28  PC29    653 non-null    float64
 29  PC30    653 non-null    float64
 30  PC31    653 non-null    float64
 31  PC32    653 non-null    float64
 32  PC33    653 non-null    float64
 33  PC34    653 non-null    float64
 34  PC35    653 non-null    float64
 35  PC36    653 non-null    float64
 36  PC37    653 non-null    float64
 37  PC38    653 non-null    float64
 38  PC39    653 non-null    float64
 39  PC40    653 non-null    float64
 40  PC41    653 non-null    float64
 41  PC42    653 non-null    float64
 42  PC43    653 non-null    float64
 43  PC44    653 non-null    float64
 44  PC45    653 non-null    float64
 45  PC46    653 non-null    float64
 46  PC47    653 non-null    float64
 47  PC48    653 non-null    float64
 48  PC49    653 non-null    float64
 49  PC50    653 non-null    float64
 50  PC51    653 non-null    float64
 51  PC52    653 non-null    float64
 52  PC53    653 non-null    float64
 53  PC54    653 non-null    float64
 54  PC55    653 non-null    float64
 55  PC56    653 non-null    float64
 56  PC57    653 non-null    float64
 57  PC58    653 non-null    float64
 58  PC59    653 non-null    float64
 59  PC60    653 non-null    float64
 60  PC61    653 non-null    float64
 61  PC62    653 non-null    float64
 62  PC63    653 non-null    float64
 63  PC64    653 non-null    float64
 64  PC65    653 non-null    float64
 65  PC66    653 non-null    float64
 66  PC67    653 non-null    float64
 67  PC68    653 non-null    float64
 68  PC69    653 non-null    float64
 69  PC70    653 non-null    float64
 70  PC71    653 non-null    float64
 71  PC72    653 non-null    float64
 72  PC73    653 non-null    float64
 73  PC74    653 non-null    float64
 74  PC75    653 non-null    float64
 75  PC76    653 non-null    float64
 76  PC77    653 non-null    float64
dtypes: float64(77)
memory usage: 392.9 KB
In [109]:
sns.catplot(data = pc_scores_df.iloc[:, :10], kind='box', aspect=3)

plt.show()
In [110]:
def calc_pca_contrib(load_mat):
    # square each element in the loadings matrix
    load_mat_sq = load_mat ** 2
    # sum the square loadings for each PC
    sum_load_squares = load_mat_sq.sum(axis=0)
    # divide the square loadings by the sum of the squared loadings per PC
    contrib_mat = load_mat_sq / sum_load_squares
    
    return(contrib_mat)
In [111]:
fig, ax = plt.subplots(figsize=(36, 18))

sns.heatmap( data = np.transpose( calc_pca_contrib( pca_object.components_) ) > (1 / pc_scores.shape[1]), 
            xticklabels=pc_scores_df.iloc[:, :len(num_vars)].columns.tolist(),
            yticklabels=num_vars,
            vmin=0, vmax=1)

plt.show()
Continuous preprocessor and pipelines for pairwise polynomials with PCA¶
In [112]:
numeric_transform_pca = Pipeline( steps=[('std_input', StandardScaler()),
                                        ('pca', PCA(n_components=15)),
                                        ('make_poly', PolynomialFeatures(degree=2, include_bias=False))])
In [113]:
complex_transform = ColumnTransformer( transformers=[('num', numeric_transform_pca, num_vars),
                                                    ('cat', categorical_transform, categorical_inputs)])
In [114]:
complex_transform.transformers
Out[114]:
[('num',
  Pipeline(steps=[('std_input', StandardScaler()), ('pca', PCA(n_components=15)),
                  ('make_poly', PolynomialFeatures(include_bias=False))]),
  ['total_ms_tp000_sqrt',
   'mw_tp000_sqrt',
   'mwc_tp000_sqrt',
   'mcl_tp000_sqrt',
   'mcr_tp000_sqrt',
   'mm_tp000_sqrt',
   'ks_tp000_sqrt',
   'total_ms_tp010_sqrt',
   'mw_tp010_sqrt',
   'mwc_tp010_sqrt',
   'mcl_tp010_sqrt',
   'mcr_tp010_sqrt',
   'mm_tp010_sqrt',
   'ks_tp010_sqrt',
   'total_ms_tp020_sqrt',
   'mw_tp020_sqrt',
   'mwc_tp020_sqrt',
   'mcl_tp020_sqrt',
   'mcr_tp020_sqrt',
   'mm_tp020_sqrt',
   'ks_tp020_sqrt',
   'total_ms_tp030_sqrt',
   'mw_tp030_sqrt',
   'mwc_tp030_sqrt',
   'mcl_tp030_sqrt',
   'mcr_tp030_sqrt',
   'mm_tp030_sqrt',
   'ks_tp030_sqrt',
   'total_ms_tp040_sqrt',
   'mw_tp040_sqrt',
   'mwc_tp040_sqrt',
   'mcl_tp040_sqrt',
   'mcr_tp040_sqrt',
   'mm_tp040_sqrt',
   'ks_tp040_sqrt',
   'total_ms_tp050_sqrt',
   'mw_tp050_sqrt',
   'mwc_tp050_sqrt',
   'mcl_tp050_sqrt',
   'mcr_tp050_sqrt',
   'mm_tp050_sqrt',
   'ks_tp050_sqrt',
   'total_ms_tp060_sqrt',
   'mw_tp060_sqrt',
   'mwc_tp060_sqrt',
   'mcl_tp060_sqrt',
   'mcr_tp060_sqrt',
   'mm_tp060_sqrt',
   'ks_tp060_sqrt',
   'total_ms_tp070_sqrt',
   'mw_tp070_sqrt',
   'mwc_tp070_sqrt',
   'mcl_tp070_sqrt',
   'mcr_tp070_sqrt',
   'mm_tp070_sqrt',
   'ks_tp070_sqrt',
   'total_ms_tp080_sqrt',
   'mw_tp080_sqrt',
   'mwc_tp080_sqrt',
   'mcl_tp080_sqrt',
   'mcr_tp080_sqrt',
   'mm_tp080_sqrt',
   'ks_tp080_sqrt',
   'total_ms_tp090_sqrt',
   'mw_tp090_sqrt',
   'mwc_tp090_sqrt',
   'mcl_tp090_sqrt',
   'mcr_tp090_sqrt',
   'mm_tp090_sqrt',
   'ks_tp090_sqrt',
   'total_ms_tp100_sqrt',
   'mw_tp100_sqrt',
   'mwc_tp100_sqrt',
   'mcl_tp100_sqrt',
   'mcr_tp100_sqrt',
   'mm_tp100_sqrt',
   'ks_tp100_sqrt']),
 ('cat',
  Pipeline(steps=[('dummy', OneHotEncoder(drop='first'))]),
  ['actv_grp'])]
In [115]:
complex_transform.fit_transform( s2_df ).shape
Out[115]:
(653, 144)

No interactions - that is why the features do not equal the dmatrices

In [116]:
interaction_transform = Pipeline( steps=[ ('prepro', complex_transform),
                                            ('make_interact', PolynomialFeatures(degree=2, interaction_only=True, include_bias=False))])
In [117]:
interaction_transform.fit_transform( s2_df ).shape
Out[117]:
(653, 10440)
In [118]:
default_enet_complex_wflow = Pipeline( steps=[('prepro', complex_transform),
                                              ('enet', enet_default)])
In [119]:
#default_enet_complex_cv_scores = cross_val_score( default_enet_complex_wflow, s2_df, y_train, cv=my_cv )
In [120]:
numeric_transform_pca_b = Pipeline( steps=[('std_input', StandardScaler()),
                                        ('pca', PCA(n_components=15)),
                                        ('make_poly', PolynomialFeatures(degree=2, include_bias=False)),
                                        ('std_features', StandardScaler())])
In [121]:
complex_transform_b = ColumnTransformer( transformers=[('num', numeric_transform_pca_b, num_vars),
                                                    ('cat', categorical_transform, categorical_inputs)])
In [122]:
default_enet_complex_wflow_b = Pipeline( steps=[('prepro', complex_transform_b),
                                              ('enet', enet_default)])
In [123]:
#default_enet_complex_cv_scores_b = cross_val_score( default_enet_complex_wflow_b, s2_df, y_train, cv=my_cv )
In [ ]: